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Angle Side Angle (ASA)

Angle Side Angle (ASA)
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2014-07-15 06:49
TriangleAngleGeometric Construction
In collections Triangle Congruence Geometry - Triangle Congruence
This example illustrates the Angle Side Angle (ASA) theorem, which states that if two triangles have two pairs of equal angles and the included side, then the triangles are congruent. Key mathematical concepts include triangle congruence, angle and side relationships. It uses commands like Line, Point, Circle, Segment, Angle, Rotate, Ray in GeoGebra. Suitable for middle school and above students to learn triangle congruence through geometric construction.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Point(a) → C
  3. Point(a) → D
  4. Point(a) → E
  5. Point(a) → F
  6. Point(a) → H
  7. Circle(C, D) → c
  8. Circle(E, F) → d
  9. Point(c) → I
  10. Point(d) → J
  11. Segment(C, I) → b
  12. Angle(D, C, I) → α
  13. Angle(F, E, J) → β
  14. Segment(C, D) → g
  15. Segment(E, J) → h
  16. Segment(E, F) → i
  17. Point(a) → G
  18. Point(a) → L
  19. Segment(G, L) → e
  20. Point(Circle[K, abs(e)]) → M
  21. Segment(K, M) → j
  22. Point(Circle[N, abs(e)]) → O
  23. Segment(N, O) → k
  24. Rotate(M, α, K) → M'
  25. Angle(M, K, M') → γ
  26. Rotate(O, α, N) → O'
  27. Angle(O, N, O') → δ
  28. Rotate(K, (-β), M) → K'
  29. Angle(K, M, K') → ε
  30. Rotate(N, (-β), O) → N'
  31. Angle(N, O, N') → ζ
  32. Ray(M, K') → m
  33. Ray(K, M') → n
  34. Ray(N, O') → p
  35. Ray(O, N') → q
  36. Point(m) → P
  37. Point(n) → Q
  38. Point(q) → R
  39. Point(p) → S
  40. Segment(K, Q) → r
  41. Segment(P, M) → s
  42. Segment(N, S) → t
  43. Segment(R, O) → a_1

AI Drawing Prompt Reference

Draw two triangles ABC and DEF with ∠ACB = ∠DFE and BC = EF. Construct corresponding sides and angles of triangles ABC and DEF, including line segments BC and EF, angles ∠ACB and ∠DFE, and line segments AB, AC, DE, DF. Then construct corresponding points of triangles ABC and DEF, such as points G and L, line segment GL, and rotate points M and O to form angles ∠M'KM and ∠O'NO. Finally, connect points P, Q, R, and S to form line segments PQ and RS.
The prompt above was compiled from the original drawing commands and is for reference only.